Minimax identity with robust utility functional for a nonconcave utility

The minimax identity for a nondecreasing upper-semicontinuous utility function satisfying mild growth assumption is studied. In contrast to the classical setting, concavity of not asumed. By considering concave envelope function, equalities and inequalities between robust functionals an initial its concavification are obtained. Furthermore, similar proved in case implementing upper bound on final endowment model.